Related papers: Completely random measures for modeling power laws…
While previous works have shown that an overwhelming number of scale-free networks are sparse, there still exist some real-world networks including social networks, urban networks, information networks, which are by observation dense. In…
Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…
Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree…
We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollob\'as et al. [2007], we show that i) the class of models is…
Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous,…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
Recent researches on complex systems highlighted the so-called super-linear growth phenomenon. As the system size $P$ measured as population in cities or active users in online communities increases, the total activities $X$ measured as GDP…
Social networks have a small number of large hubs, and a large number of small dense communities. We propose a generative model that captures both hub and dense structures. Based on recent results about graphons on line graphs, our model is…
Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…
Large real-world graphs tend to be sparse, but they often contain many densely connected subgraphs and exhibit high clustering coefficients. While recent random graph models can capture this sparsity, they ignore the local density, or vice…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…